Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds

• Verfasst von: Cao, Yalong [VerfasserIn]
• Verfasst von: Oberdieck, Georg [VerfasserIn]
• Verfasst von: Toda, Yukinobu [VerfasserIn]
• Titel: Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
• Verf.angabe: Yalong Cao, Georg Oberdieck, Yukinobu Toda
• E-Jahr: 2022
• Jahr: 29 October 2022
• Umfang: 44 S.
• Fussnoten: Gesehen am 12.12.2024
• Titel Quelle: Enthalten in: Advances in mathematics
• Ort Quelle: Amsterdam [u.a.] : Elsevier, 1961
• Jahr Quelle: 2022
• Band/Heft Quelle: 408(2022), B, Artikel-ID 108605, Seite 1-44
• ISSN Quelle: 1090-2082
• DOI: doi:10.1016/j.aim.2022.108605
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Gopakumar-Vafa type invariants
• Sach-SW: Holomorphic symplectic 4-folds
• Sach-SW: Stable pairs
• K10plus-PPN: 1912165775

Abstract

As an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds, Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau 4-fold X using Gromov-Witten theory. When X is holomorphic symplectic, Gromov-Witten invariants vanish and one can consider the corresponding reduced theory. In a companion work, we propose a definition of Gopakumar-Vafa type invariants for such a reduced theory. In this paper, we give them a sheaf theoretic interpretation via moduli spaces of stable pairs.